During its Build 2015 keynote today, Microsoft announced that Continuum will be built into Windows 10 for phones, allowing users with "select premium phones" to connect their phone to a keyboard, mouse, and external screen for a desktop-like experience.
When users connect their phone to an external monitor via HDMI, along with a Bluetooth keyboard and mouse, they'll essentially be working from a desktop environment. The UI will adapt to fit the larger display, start-menu and all. As far as apps are concerned, it looks like this is where the universal model is going to pay off. During the demo, Microsoft showed off Office running from a phone on an external screen, and it looked very much like the PC app.
Overall, this looks like an amazing use of Continuum, showing off the universality of Windows 10 across devices. Given the right equipment, you're basically carrying a PC in your pocket at all times. It is important to note, however, that Continuum for phones will be limited to "select premium phones." So it's unlikely to come to low-end Lumia devices.